ung.firstdiff.max <- diff(rev(bm_quants_ung[5,]), lag = 1)
ung.firstdiff.median <- diff(rev(bm_quants_ung[3,]), lag = 1)
ung.firstdiff.min <- diff(rev(bm_quants_ung[1,]), lag = 1)
ung.firstdiff.mat <- cbind(Time = rev(intervals$ageBase[1:(nrow(intervals)-1)]),ung.firstdiff.max, ung.firstdiff.median, ung.firstdiff.min)

rownames(ung.firstdiff.mat) <- paste(rev(intervals$ageBase[1:(nrow(intervals)-1)]), "Ma", sep = " ")


ung.firstdiff.mat
##       Time ung.firstdiff.max ung.firstdiff.median ung.firstdiff.min
## 65 Ma   65       0.092557817         0.0452368023       0.000000000
## 63 Ma   63       0.141301489         0.2582402581       0.147167922
## 61 Ma   61       0.000000000         0.0699986182       0.140223432
## 59 Ma   59       0.000000000         0.0000000000       0.000000000
## 57 Ma   57       0.349167481         0.1762605675      -0.042768768
## 55 Ma   55       0.489711588         0.1029232635       0.000000000
## 53 Ma   53       0.000000000         0.0029583219       0.000000000
## 51 Ma   51       0.571450342         0.0314626679       0.000000000
## 49 Ma   49       0.177954666         0.1091727281       0.000000000
## 47 Ma   47       0.051682296         0.1791715371       0.064273300
## 45 Ma   45       0.056038575         0.0326878381       0.528751572
## 43 Ma   43       0.000000000         0.0232737076       0.122214919
## 41 Ma   41       0.127287814         0.2259501615      -0.320054622
## 39 Ma   39       0.064135408         0.1459134775       0.126212462
## 37 Ma   37       0.190803655         0.0644432997       0.000000000
## 35 Ma   35       0.000000000         0.0359998527       0.095393249
## 33 Ma   33      -0.400249056         0.2164271975       0.034457040
## 31 Ma   31       0.045182971        -0.1092693663       0.126724371
## 29 Ma   29       0.045182971         0.0045328455       0.000000000
## 27 Ma   27       0.206582820        -0.0037803730       0.000000000
## 25 Ma   25      -0.144355262         0.1006249720       0.000000000
## 23 Ma   23       0.013345247         0.1022657148       0.000000000
## 21 Ma   21       0.002111031         0.0446100476       0.069708633
## 19 Ma   19       0.008110824         0.0048524924      -0.008510178
## 17 Ma   17       0.000000000         0.0005592086       0.117810209
## 15 Ma   15       0.000000000         0.0238968243       0.000000000
## 13 Ma   13       0.000000000         0.0360707725       0.205272062
## 11 Ma   11       0.107175255        -0.0058689393       0.097808216
## 9 Ma     9       0.000000000        -0.0079260911       0.000000000
## 7 Ma     7       0.000000000         0.0119336570       0.000000000
## 5 Ma     5      -0.115286079         0.2031847543       0.000000000
## 3 Ma     3      -0.002111031         0.0728081257       0.207886020

pred.firstdiff.max <- diff(rev(bm_quantsPred_allcarniv[5,]), lag = 1)
pred.firstdiff.median <- diff(rev(bm_quantsPred_allcarniv[3,]), lag = 1)
pred.firstdiff.min <- diff(rev(bm_quantsPred_allcarniv[1,]), lag = 1)
pred.firstdiff.mat <- cbind(Time= rev(intervals$ageBase[1:(nrow(intervals)-1)]), pred.firstdiff.max, pred.firstdiff.median, pred.firstdiff.min)

rownames(pred.firstdiff.mat) <- paste(rev(intervals$ageBase[1:(nrow(intervals)-1)]), "Ma", sep = " ")

pred.firstdiff.mat
##       Time pred.firstdiff.max pred.firstdiff.median pred.firstdiff.min
## 63 Ma   63         0.11051477          -0.064389602        -0.46061401
## 61 Ma   61         0.51835829           0.194058596         0.00000000
## 59 Ma   59         0.00000000           0.086902747         0.00000000
## 57 Ma   57         0.65761266           0.352184166         0.23383005
## 55 Ma   55         0.00000000          -0.142881358         0.00000000
## 53 Ma   53         0.00000000          -0.050390953         0.00000000
## 51 Ma   51         0.06949124           0.136430584         0.00000000
## 49 Ma   49         0.00000000          -0.086941781         0.17786028
## 47 Ma   47         0.00000000           0.188459429         0.03611801
## 45 Ma   45         0.00000000           0.053800447         0.07263397
## 43 Ma   43        -0.47659314           0.000000000         0.15545135
## 41 Ma   41         0.25593371           0.264793830         0.32197521
## 39 Ma   39         0.00000000           0.041810564         0.22791018
## 37 Ma   37         0.00000000           0.000000000        -0.40614309
## 35 Ma   35         0.18062514           0.362167899         0.00000000
## 33 Ma   33         0.13600314           0.071707437         0.35605018
## 31 Ma   31         0.00000000          -0.001176597        -0.54569234
## 29 Ma   29         0.00000000          -0.001176597         0.00000000
## 27 Ma   27         0.24534895          -0.002353194         0.00000000
## 25 Ma   25         0.00000000           0.035761393         0.25566786
## 23 Ma   23         0.27895842           0.150276188         0.00000000
## 21 Ma   21         0.01784590           0.141928676         0.00000000
## 19 Ma   19         0.20211174           0.000000000         0.13653881
## 17 Ma   17         0.00000000          -0.033651455        -0.34630681
## 15 Ma   15         0.00000000          -0.018633600         0.00000000
## 13 Ma   13         0.00000000           0.109551936         0.35232484
## 11 Ma   11         0.00000000           0.087608314        -0.25464684
## 9 Ma     9         0.00000000          -0.035833794        -0.23342601
## 7 Ma     7        -0.17236488           0.012219300         0.00000000
## 5 Ma     5        -0.13594862          -0.075094149         0.00000000
## 3 Ma     3         0.00000000          -0.173542316        -0.10219561

#plot differences against each other

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat[, "pred.firstdiff.max"] ~ ung.firstdiff.mat[, 
##     "ung.firstdiff.max"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52273 -0.06588 -0.04614  0.08315  0.53099 
## 
## Coefficients:
##                                          Estimate Std. Error t value
## (Intercept)                               0.04614    0.03772   1.223
## ung.firstdiff.mat[, "ung.firstdiff.max"]  0.23050    0.20444   1.127
##                                          Pr(>|t|)
## (Intercept)                                 0.231
## ung.firstdiff.mat[, "ung.firstdiff.max"]    0.269
## 
## Residual standard error: 0.197 on 29 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.04199,    Adjusted R-squared:  0.008958 
## F-statistic: 1.271 on 1 and 29 DF,  p-value: 0.2688

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat[, "pred.firstdiff.median"] ~ 
##     ung.firstdiff.mat[, "ung.firstdiff.median"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.22617 -0.06247 -0.02433  0.07826  0.31942 
## 
## Coefficients:
##                                             Estimate Std. Error t value
## (Intercept)                                  0.03309    0.02977   1.111
## ung.firstdiff.mat[, "ung.firstdiff.median"]  0.26828    0.27335   0.981
##                                             Pr(>|t|)
## (Intercept)                                    0.275
## ung.firstdiff.mat[, "ung.firstdiff.median"]    0.334
## 
## Residual standard error: 0.1277 on 29 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.03215,    Adjusted R-squared:  -0.001225 
## F-statistic: 0.9633 on 1 and 29 DF,  p-value: 0.3345

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat[, "pred.firstdiff.min"] ~ ung.firstdiff.mat[, 
##     "ung.firstdiff.min"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52181 -0.01716 -0.01716  0.16929  0.40165 
## 
## Coefficients:
##                                          Estimate Std. Error t value
## (Intercept)                               0.01716    0.04419   0.388
## ung.firstdiff.mat[, "ung.firstdiff.min"] -0.32389    0.31761  -1.020
##                                          Pr(>|t|)
## (Intercept)                                 0.701
## ung.firstdiff.mat[, "ung.firstdiff.min"]    0.316
## 
## Residual standard error: 0.2258 on 29 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.03462,    Adjusted R-squared:  0.001331 
## F-statistic:  1.04 on 1 and 29 DF,  p-value: 0.3163

First Differences using NALMA bins

#get color gradient for 2Ma Bins
nalma.mark <- read.csv("/Users/emdoughty/Downloads/PPP_summary.csv")
nalma.mark <- nalma.mark[,1:3]
nalma.add  <- rbind(c("Aquilian", 84, 70),c("Lancian", 70, 66),c("Puercan", 66, 64.81)); colnames(nalma.add) <- colnames(nalma.mark)
nalma.mark <- rbind(nalma.mark, nalma.add)
nalma.mark[,2] <- as.numeric(nalma.mark[,2])
nalma.mark[,3] <- as.numeric(nalma.mark[,3])
nalma.mark <- nalma.mark[order(as.numeric(nalma.mark$Max_age), decreasing = TRUE),]
rownames(nalma.mark) <- nalma.mark$NALMA_Subdivision
colnames(nalma.mark) <- c("NALMA_Subdivision", "ageBase","ageTop")
nalma.mark <- nalma.mark[,-1]
nalma.mark <- nalma.mark[,c(2,1)]

intervals <- nalma.mark

Ungulate First Differences for Max, Median, and Min

##                                                ung.firstdiff.max_NALMA
## Aquilian-Lancian                                                    NA
## Lancian-Puercan                                                     NA
## Puercan-Torrejonian                                         0.23385931
## Torrejonian-Tiffanian                                       0.00000000
## Tiffanian-Clarkforkian                                      0.00000000
## Clarkforkian-Early Wasatchian                               0.34916748
## Early Wasatchian-Middle Wascatchian                         0.00000000
## Middle Wascatchian-Late Wasatchian                          0.00000000
## Late Wasatchian-Early Bridgerian                            0.88320726
## Early Bridgerian-Middle Bridgerian                          0.00000000
## Middle Bridgerian-Late Bridgerian                           0.00000000
## Late Bridgerian-Early Uintan                                0.28882715
## Early Uintan-Late Uintan                                    0.30209086
## Late Uintan-Duchesnean                                      0.06413541
## Duchesnean-Early Chadronian                                 0.13471675
## Early Chadronian-Middle Chadronian                          0.02637186
## Middle Chadronian-Late Chadronian                           0.05943008
## Late Chadronian-Orellan                                    -0.42996410
## Orellan-Whitneyan                                           0.09036594
## Whitneyan-Early early Arikareean                            0.00000000
## Early early Arikareean-Late early Arikareean                0.20658282
## Late early Arikareean-Early late Arikareean                -0.12078816
## Early late Arikareean-Late late Arikareean                  0.00000000
## Late late Arikareean-Early Hemingfordian                    0.00000000
## Early Hemingfordian-Late Hemingfordian                      0.00000000
## Late Hemingfordian-Early Barstovian                         0.00000000
## Early Barstovian-Late Barstovian                            0.00000000
## Late Barstovian-Early Clarendonian                          0.00000000
## Early Clarendonian-Middle Clarendonian                      0.10717525
## Middle Clarendonian-Late Clarendonian                       0.00000000
## Late Clarendonian-Early early Hemphillian                   0.00000000
## Early early Hemphillian-Late early Hemphillian              0.00000000
## Late early Hemphillian-Late Hemphillian                     0.00000000
## Late Hemphillian-Latest Hemphillian                         0.00000000
## Latest Hemphillian-Early Blancan                           -0.11739711
## Early Blancan-Late Blancan                                 -0.08065057
## Late Blancan-Early Ivingtonian                             -0.11291914
## Early Ivingtonian-Middle Ivingtonian                       -0.18080200
## Middle Ivingtonian-Rancholabrean                            0.00000000
## Rancholabrean-Holocene                                     -0.13342161
##                                                ung.firstdiff.median_NALMA
## Aquilian-Lancian                                                       NA
## Lancian-Puercan                                                        NA
## Puercan-Torrejonian                                           0.035523620
## Torrejonian-Tiffanian                                         0.257288801
## Tiffanian-Clarkforkian                                        0.123148976
## Clarkforkian-Early Wasatchian                                 0.188738040
## Early Wasatchian-Middle Wascatchian                           0.046809721
## Middle Wascatchian-Late Wasatchian                            0.000000000
## Late Wasatchian-Early Bridgerian                              0.010432118
## Early Bridgerian-Middle Bridgerian                            0.088845720
## Middle Bridgerian-Late Bridgerian                             0.262745332
## Late Bridgerian-Early Uintan                                  0.143764575
## Early Uintan-Late Uintan                                     -0.065294750
## Late Uintan-Duchesnean                                        0.377906609
## Duchesnean-Early Chadronian                                  -0.158543878
## Early Chadronian-Middle Chadronian                            0.170290044
## Middle Chadronian-Late Chadronian                             0.058182649
## Late Chadronian-Orellan                                       0.014640123
## Orellan-Whitneyan                                             0.185838936
## Whitneyan-Early early Arikareean                             -0.102084131
## Early early Arikareean-Late early Arikareean                  0.118929797
## Late early Arikareean-Early late Arikareean                   0.055210795
## Early late Arikareean-Late late Arikareean                    0.015841381
## Late late Arikareean-Early Hemingfordian                      0.005283240
## Early Hemingfordian-Late Hemingfordian                        0.000000000
## Late Hemingfordian-Early Barstovian                           0.017581878
## Early Barstovian-Late Barstovian                              0.013492076
## Late Barstovian-Early Clarendonian                            0.004774752
## Early Clarendonian-Middle Clarendonian                        0.036058856
## Middle Clarendonian-Late Clarendonian                         0.006596664
## Late Clarendonian-Early early Hemphillian                     0.001211235
## Early early Hemphillian-Late early Hemphillian                0.036618775
## Late early Hemphillian-Late Hemphillian                      -0.000425132
## Late Hemphillian-Latest Hemphillian                           0.000425132
## Latest Hemphillian-Early Blancan                              0.173937973
## Early Blancan-Late Blancan                                    0.171482261
## Late Blancan-Early Ivingtonian                               -0.060081671
## Early Ivingtonian-Middle Ivingtonian                          0.030670317
## Middle Ivingtonian-Rancholabrean                             -0.001731479
## Rancholabrean-Holocene                                        0.017013785
##                                                ung.firstdiff.min_NALMA
## Aquilian-Lancian                                                    NA
## Lancian-Puercan                                                     NA
## Puercan-Torrejonian                                        0.000000000
## Torrejonian-Tiffanian                                      0.224575223
## Tiffanian-Clarkforkian                                     0.062816131
## Clarkforkian-Early Wasatchian                             -0.042768768
## Early Wasatchian-Middle Wascatchian                        0.000000000
## Middle Wascatchian-Late Wasatchian                         0.000000000
## Late Wasatchian-Early Bridgerian                           0.000000000
## Early Bridgerian-Middle Bridgerian                         0.000000000
## Middle Bridgerian-Late Bridgerian                          0.064273300
## Late Bridgerian-Early Uintan                               0.000000000
## Early Uintan-Late Uintan                                   0.330911869
## Late Uintan-Duchesnean                                     0.390257752
## Duchesnean-Early Chadronian                               -0.264045289
## Early Chadronian-Middle Chadronian                         0.096949511
## Middle Chadronian-Late Chadronian                          0.000000000
## Late Chadronian-Orellan                                    0.026854601
## Orellan-Whitneyan                                          0.006046177
## Whitneyan-Early early Arikareean                           0.126724371
## Early early Arikareean-Late early Arikareean               0.000000000
## Late early Arikareean-Early late Arikareean                0.000000000
## Early late Arikareean-Late late Arikareean                 0.555116398
## Late late Arikareean-Early Hemingfordian                  -0.092112897
## Early Hemingfordian-Late Hemingfordian                    -0.166668858
## Late Hemingfordian-Early Barstovian                       -0.117325977
## Early Barstovian-Late Barstovian                           0.000000000
## Late Barstovian-Early Clarendonian                         0.107463845
## Early Clarendonian-Middle Clarendonian                     0.000000000
## Middle Clarendonian-Late Clarendonian                      0.000000000
## Late Clarendonian-Early early Hemphillian                  0.000000000
## Early early Hemphillian-Late early Hemphillian             0.195616433
## Late early Hemphillian-Late Hemphillian                    0.000000000
## Late Hemphillian-Latest Hemphillian                        0.000000000
## Latest Hemphillian-Early Blancan                           0.135004884
## Early Blancan-Late Blancan                                 0.184278196
## Late Blancan-Early Ivingtonian                            -0.111397060
## Early Ivingtonian-Middle Ivingtonian                      -0.286049550
## Middle Ivingtonian-Rancholabrean                           0.000000000
## Rancholabrean-Holocene                                     0.682026670

Predators First Differences for Max, Median, and Min

##                                                pred.firstdiff.max_NALMA
## Aquilian-Lancian                                                     NA
## Lancian-Puercan                                                      NA
## Puercan-Torrejonian                                                  NA
## Torrejonian-Tiffanian                                        0.62887306
## Tiffanian-Clarkforkian                                       0.05457046
## Clarkforkian-Early Wasatchian                                0.60304220
## Early Wasatchian-Middle Wascatchian                          0.00000000
## Middle Wascatchian-Late Wasatchian                           0.00000000
## Late Wasatchian-Early Bridgerian                             0.06949124
## Early Bridgerian-Middle Bridgerian                           0.00000000
## Middle Bridgerian-Late Bridgerian                            0.00000000
## Late Bridgerian-Early Uintan                                 0.00000000
## Early Uintan-Late Uintan                                     0.00000000
## Late Uintan-Duchesnean                                      -0.22065943
## Duchesnean-Early Chadronian                                  0.00000000
## Early Chadronian-Middle Chadronian                           0.00000000
## Middle Chadronian-Late Chadronian                            0.00000000
## Late Chadronian-Orellan                                      0.31662828
## Orellan-Whitneyan                                            0.00000000
## Whitneyan-Early early Arikareean                             0.00000000
## Early early Arikareean-Late early Arikareean                 0.52430737
## Late early Arikareean-Early late Arikareean                  0.01784590
## Early late Arikareean-Late late Arikareean                   0.00000000
## Late late Arikareean-Early Hemingfordian                     0.00000000
## Early Hemingfordian-Late Hemingfordian                       0.00000000
## Late Hemingfordian-Early Barstovian                          0.07937900
## Early Barstovian-Late Barstovian                             0.12273274
## Late Barstovian-Early Clarendonian                           0.00000000
## Early Clarendonian-Middle Clarendonian                       0.00000000
## Middle Clarendonian-Late Clarendonian                        0.00000000
## Late Clarendonian-Early early Hemphillian                    0.00000000
## Early early Hemphillian-Late early Hemphillian              -0.21995764
## Late early Hemphillian-Late Hemphillian                      0.00000000
## Late Hemphillian-Latest Hemphillian                          0.00000000
## Latest Hemphillian-Early Blancan                            -0.12467978
## Early Blancan-Late Blancan                                   0.03632392
## Late Blancan-Early Ivingtonian                               0.00000000
## Early Ivingtonian-Middle Ivingtonian                         0.00000000
## Middle Ivingtonian-Rancholabrean                             0.00000000
## Rancholabrean-Holocene                                      -0.14480914
##                                                pred.firstdiff.median_NALMA
## Aquilian-Lancian                                                        NA
## Lancian-Puercan                                                         NA
## Puercan-Torrejonian                                                     NA
## Torrejonian-Tiffanian                                           0.31844166
## Tiffanian-Clarkforkian                                          0.16082324
## Clarkforkian-Early Wasatchian                                   0.14163677
## Early Wasatchian-Middle Wascatchian                            -0.05039095
## Middle Wascatchian-Late Wasatchian                              0.05039095
## Late Wasatchian-Early Bridgerian                                0.07129736
## Early Bridgerian-Middle Bridgerian                             -0.07129736
## Middle Bridgerian-Late Bridgerian                               0.00000000
## Late Bridgerian-Early Uintan                                   -0.06575526
## Early Uintan-Late Uintan                                        0.26073158
## Late Uintan-Duchesnean                                          0.30259485
## Duchesnean-Early Chadronian                                    -0.04181056
## Early Chadronian-Middle Chadronian                              0.04181056
## Middle Chadronian-Late Chadronian                               0.05557376
## Late Chadronian-Orellan                                         0.39109105
## Orellan-Whitneyan                                              -0.15620434
## Whitneyan-Early early Arikareean                                0.20552489
## Early early Arikareean-Late early Arikareean                    0.06663472
## Late early Arikareean-Early late Arikareean                     0.08744343
## Early late Arikareean-Late late Arikareean                      0.12568647
## Late late Arikareean-Early Hemingfordian                        0.02262531
## Early Hemingfordian-Late Hemingfordian                         -0.06566660
## Late Hemingfordian-Early Barstovian                             0.03399890
## Early Barstovian-Late Barstovian                               -0.02459022
## Late Barstovian-Early Clarendonian                              0.20840635
## Early Clarendonian-Middle Clarendonian                         -0.18029296
## Middle Clarendonian-Late Clarendonian                           0.19471423
## Late Clarendonian-Early early Hemphillian                      -0.04197578
## Early early Hemphillian-Late early Hemphillian                  0.01313324
## Late early Hemphillian-Late Hemphillian                        -0.01313324
## Late Hemphillian-Latest Hemphillian                             0.12308693
## Latest Hemphillian-Early Blancan                               -0.27893342
## Early Blancan-Late Blancan                                      0.05709012
## Late Blancan-Early Ivingtonian                                 -0.09722669
## Early Ivingtonian-Middle Ivingtonian                            0.09722669
## Middle Ivingtonian-Rancholabrean                                0.06737628
## Rancholabrean-Holocene                                         -0.56298745
##                                                pred.firstdiff.min_NALMA
## Aquilian-Lancian                                                     NA
## Lancian-Puercan                                                      NA
## Puercan-Torrejonian                                                  NA
## Torrejonian-Tiffanian                                         0.0000000
## Tiffanian-Clarkforkian                                        0.2338300
## Clarkforkian-Early Wasatchian                                 0.0000000
## Early Wasatchian-Middle Wascatchian                           0.0000000
## Middle Wascatchian-Late Wasatchian                            0.0000000
## Late Wasatchian-Early Bridgerian                              0.0000000
## Early Bridgerian-Middle Bridgerian                            0.1778603
## Middle Bridgerian-Late Bridgerian                             0.0000000
## Late Bridgerian-Early Uintan                                  0.0000000
## Early Uintan-Late Uintan                                      0.1087520
## Late Uintan-Duchesnean                                        0.7053367
## Duchesnean-Early Chadronian                                  -0.4061431
## Early Chadronian-Middle Chadronian                            0.0000000
## Middle Chadronian-Late Chadronian                             0.0000000
## Late Chadronian-Orellan                                       0.1085306
## Orellan-Whitneyan                                            -0.2981728
## Whitneyan-Early early Arikareean                              0.0000000
## Early early Arikareean-Late early Arikareean                  0.2556679
## Late early Arikareean-Early late Arikareean                   0.0000000
## Early late Arikareean-Late late Arikareean                    0.1365388
## Late late Arikareean-Early Hemingfordian                      0.0000000
## Early Hemingfordian-Late Hemingfordian                        0.0000000
## Late Hemingfordian-Early Barstovian                          -0.3463068
## Early Barstovian-Late Barstovian                              0.0000000
## Late Barstovian-Early Clarendonian                            0.3523248
## Early Clarendonian-Middle Clarendonian                       -0.4880729
## Middle Clarendonian-Late Clarendonian                         0.0000000
## Late Clarendonian-Early early Hemphillian                     0.0000000
## Early early Hemphillian-Late early Hemphillian                0.0000000
## Late early Hemphillian-Late Hemphillian                       0.0000000
## Late Hemphillian-Latest Hemphillian                           0.0000000
## Latest Hemphillian-Early Blancan                              0.0000000
## Early Blancan-Late Blancan                                   -0.1021956
## Late Blancan-Early Ivingtonian                                0.0000000
## Early Ivingtonian-Middle Ivingtonian                          0.0000000
## Middle Ivingtonian-Rancholabrean                              0.0000000
## Rancholabrean-Holocene                                        0.0000000

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat_NALMA[, "pred.firstdiff.max_NALMA"] ~ 
##     ung.firstdiff.mat_NALMA[, "ung.firstdiff.max_NALMA"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.27169 -0.05470 -0.04206 -0.01676  0.58681 
## 
## Coefficients:
##                                                      Estimate Std. Error
## (Intercept)                                           0.04206    0.03082
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.max_NALMA"]  0.13990    0.15577
##                                                      t value Pr(>|t|)
## (Intercept)                                            1.365    0.181
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.max_NALMA"]   0.898    0.375
## 
## Residual standard error: 0.1843 on 35 degrees of freedom
##   (3 observations deleted due to missingness)
## Multiple R-squared:  0.02253,    Adjusted R-squared:  -0.005402 
## F-statistic: 0.8066 on 1 and 35 DF,  p-value: 0.3753

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat_NALMA[, "pred.firstdiff.median_NALMA"] ~ 
##     ung.firstdiff.mat_NALMA[, "ung.firstdiff.max_NALMA"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.59769 -0.08348  0.01017  0.08751  0.36409 
## 
## Coefficients:
##                                                      Estimate Std. Error
## (Intercept)                                           0.03817    0.02940
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.max_NALMA"]  0.02599    0.14860
##                                                      t value Pr(>|t|)
## (Intercept)                                            1.298    0.203
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.max_NALMA"]   0.175    0.862
## 
## Residual standard error: 0.1758 on 35 degrees of freedom
##   (3 observations deleted due to missingness)
## Multiple R-squared:  0.0008731,  Adjusted R-squared:  -0.02767 
## F-statistic: 0.03059 on 1 and 35 DF,  p-value: 0.8622

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat_NALMA[, "pred.firstdiff.min_NALMA"] ~ 
##     ung.firstdiff.mat_NALMA[, "ung.firstdiff.max_NALMA"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.49700 -0.01794 -0.01331  0.00097  0.69465 
## 
## Coefficients:
##                                                      Estimate Std. Error
## (Intercept)                                           0.01331    0.03380
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.max_NALMA"] -0.04092    0.17085
##                                                      t value Pr(>|t|)
## (Intercept)                                            0.394    0.696
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.max_NALMA"]  -0.240    0.812
## 
## Residual standard error: 0.2022 on 35 degrees of freedom
##   (3 observations deleted due to missingness)
## Multiple R-squared:  0.001636,   Adjusted R-squared:  -0.02689 
## F-statistic: 0.05737 on 1 and 35 DF,  p-value: 0.8121

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat_NALMA[, "pred.firstdiff.max_NALMA"] ~ 
##     ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.37383 -0.04783 -0.02743 -0.00499  0.51603 
## 
## Coefficients:
##                                                         Estimate
## (Intercept)                                              0.02682
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"]  0.33435
##                                                         Std. Error t value
## (Intercept)                                                0.03464   0.774
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"]    0.28365   1.179
##                                                         Pr(>|t|)
## (Intercept)                                                0.444
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"]    0.246
## 
## Residual standard error: 0.1828 on 35 degrees of freedom
##   (3 observations deleted due to missingness)
## Multiple R-squared:  0.03818,    Adjusted R-squared:  0.0107 
## F-statistic:  1.39 on 1 and 35 DF,  p-value: 0.2464

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat_NALMA[, "pred.firstdiff.median_NALMA"] ~ 
##     ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.59526 -0.07177  0.00164  0.09341  0.35919 
## 
## Coefficients:
##                                                         Estimate
## (Intercept)                                              0.02961
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"]  0.15658
##                                                         Std. Error t value
## (Intercept)                                                0.03317   0.893
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"]    0.27160   0.576
##                                                         Pr(>|t|)
## (Intercept)                                                0.378
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"]    0.568
## 
## Residual standard error: 0.1751 on 35 degrees of freedom
##   (3 observations deleted due to missingness)
## Multiple R-squared:  0.009406,   Adjusted R-squared:  -0.0189 
## F-statistic: 0.3323 on 1 and 35 DF,  p-value: 0.568

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat_NALMA[, "pred.firstdiff.min_NALMA"] ~ 
##     ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.48325 -0.08597  0.02216  0.06986  0.47893 
## 
## Coefficients:
##                                                         Estimate
## (Intercept)                                             -0.02922
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"]  0.67642
##                                                         Std. Error t value
## (Intercept)                                                0.03570  -0.818
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"]    0.29231   2.314
##                                                         Pr(>|t|)  
## (Intercept)                                               0.4186  
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.median_NALMA"]   0.0267 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1884 on 35 degrees of freedom
##   (3 observations deleted due to missingness)
## Multiple R-squared:  0.1327, Adjusted R-squared:  0.1079 
## F-statistic: 5.355 on 1 and 35 DF,  p-value: 0.02666

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat_NALMA[, "pred.firstdiff.max_NALMA"] ~ 
##     ung.firstdiff.mat_NALMA[, "ung.firstdiff.min_NALMA"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.24399 -0.05660 -0.05660  0.00325  0.60966 
## 
## Coefficients:
##                                                      Estimate Std. Error
## (Intercept)                                           0.05660    0.03153
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.min_NALMA"] -0.16647    0.15997
##                                                      t value Pr(>|t|)  
## (Intercept)                                            1.795   0.0813 .
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.min_NALMA"]  -1.041   0.3052  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1836 on 35 degrees of freedom
##   (3 observations deleted due to missingness)
## Multiple R-squared:  0.03001,    Adjusted R-squared:  0.002297 
## F-statistic: 1.083 on 1 and 35 DF,  p-value: 0.3052

summary(best.fit)
## 
## Call:
## lm(formula = pred.firstdiff.mat_NALMA[, "pred.firstdiff.median_NALMA"] ~ 
##     ung.firstdiff.mat_NALMA[, "ung.firstdiff.min_NALMA"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.56399 -0.09298  0.00781  0.09644  0.35014 
## 
## Coefficients:
##                                                      Estimate Std. Error
## (Intercept)                                           0.04258    0.03014
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.min_NALMA"] -0.06097    0.15291
##                                                      t value Pr(>|t|)
## (Intercept)                                            1.413    0.167
## ung.firstdiff.mat_NALMA[, "ung.firstdiff.min_NALMA"]  -0.399    0.693
## 
## Residual standard error: 0.1755 on 35 degrees of freedom
##   (3 observations deleted due to missingness)
## Multiple R-squared:  0.004522,   Adjusted R-squared:  -0.02392 
## F-statistic: 0.159 on 1 and 35 DF,  p-value: 0.6925